Table of Contents Author Guidelines Submit a Manuscript
Journal of Mathematics
Volume 2013, Article ID 809748, 5 pages
http://dx.doi.org/10.1155/2013/809748
Research Article

Instability of a Fifth-Order Nonlinear Vector Delay Differential Equation with Multiple Deviating Arguments

Department of Mathematics, Faculty of Sciences, Yüzüncü Yıl University, 65080 Van, Turkey

Received 30 August 2012; Accepted 25 September 2012

Academic Editor: Beny Neta

Copyright © 2013 Cemil Tunç. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. O. C. Ezeilo, “Instability theorems for certain fifth-order differential equations,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 84, no. 2, pp. 343–350, 1978. View at Publisher · View at Google Scholar · View at MathSciNet
  2. W. Li and K. Duan, “Instability theorems for some nonlinear differential systems of fifth order,” Journal of Natural Science, vol. 17, no. 3, pp. 1–5, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. W. J. Li and Y. H. Yu, “Instability theorems for some fourth-order and fifth-order differential equations,” Journal of Xinjiang University Natural Science, vol. 7, no. 2, pp. 7–10, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. A. I. Sadek, “Instability results for certain systems of fourth and fifth order differential equations,” Applied Mathematics and Computation, vol. 145, no. 2-3, pp. 541–549, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. W. J. Sun and X. Hou, “New results about instability of some fourth and fifth order nonlinear systems,” Journal of Xinjiang University Natural Science, vol. 16, no. 4, pp. 14–17, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. A. Tiryaki, “Extension of an instability theorem for a certain fifth order differential equation,” Journal of Karadeniz Technical University, vol. 11, pp. 225–227, 1988. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. C. Tunç, “Further results on the instability of solutions of certain nonlinear vector differential equations of fifth order,” Applied Mathematics & Information Sciences, vol. 2, no. 1, pp. 51–60, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. C. Tunç, “On the instability of solutions of some fifth order nonlinear delay differential equations,” Applied Mathematics & Information Sciences, vol. 5, no. 1, pp. 112–121, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. C. Tunç, “An instability theorem for a certain fifth-order delay differential equation,” Filomat, vol. 25, no. 3, pp. 145–151, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  10. C. Tunç, “Recent advances on instability of solutions of fourth and fifth order delay differential equations with some open problems,” in World Scientific Review, vol. 9 of World Scientific Series on Nonlinear Science Series B, pp. 105–116.
  11. C. Tunç, “On the instability of solutions of nonlinear delay differential equations of fourth and fifth order,” Sains Malaysiana, vol. 40, no. 12, pp. 1455–1459, 2011. View at Google Scholar
  12. C. Tunç, “Instability result of a fifth order non-linear delay system,” Optoelectronics and Advanced Materials-Rapid Communications, vol. 5, no. 9, pp. 891–894, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. C. Tunç, “Instability for nonlinear differential equations of fifth order subject to delay,” Nonlinear Dynamics and Systems Theory, vol. 12, no. 2, pp. 207–214, 2012. View at Google Scholar · View at MathSciNet
  14. C. Tunç, “Instability of a nonlinear differential equation of fifth order with variable delay,” International Journal of Computer and Mathematical Sciences, vol. 6, pp. 73–75, 2012. View at Google Scholar
  15. C. Tunç, “Instability of solutions for nonlinear functional differential equations of fifth order with n-deviating arguments,” Buletinul Academiei de Ştiinţe a Republicii Moldova, Matematica, vol. 68, no. 1, pp. 3–14, 2012. View at Google Scholar
  16. C. Tunç and F. Erdoğan, “On the instability of solutions of certain non-autonomous vector differential equations of fifth order,” SUT Journal of Mathematics, vol. 43, no. 1, pp. 35–48, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. C. Tunç and M. Karta, “A new instability result to nonlinear vector differential equations of fifth order,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 971534, 6 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. C. Tunç and H. Şevli, “On the instability of solutions of certain fifth order nonlinear differential equations,” Memoirs on Differential Equations and Mathematical Physics, vol. 35, pp. 147–156, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. N. N. Krasovskiĭ, “On conditions of inversion of A. M. Lyapunov's theorems on instability for stationary systems of differential equations,” Doklady Akademii Nauk SSSR, vol. 101, pp. 17–20, 1955. View at Google Scholar · View at MathSciNet
  20. R. Bellman, Introduction to Matrix Analysis, vol. 19 of Classics in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1997.